de Sitter空间中具有平行平均曲率向量的紧致伪脐类时子流形

The compact pseudo-umbilical time-like submanifolds with parallel mean curvature vector in de Sitter spaces

直接推导de Sitter空间中的类时子流形的Ricci恒等式和第二基本形式长度平方的Laplacian,得到de Sitter空间中的具有平行平均曲率向量的紧致伪脐类时子流形成为全脐子流形的一些充分条件。

The submanifolds in de Sitter space is divided into space-like submanifolds, light-like submanifolds and time-like submanifolds. A lot of conclusions are Sitter space. The compact time-like submanifolds in de Sitter given for the space-like submanifolds in de space are usually converted to the spacelike submanifolds in anti-de Sitter space. By calculating the Ricci identity and the Laplacian about the squared norm of the second fundamental form for the time-like submanifolds in de Sitter space, some sufficient conditions for the compact pseudo-umbilical time-like submanifold with parallel mean curvature vector in de Sitter space are given directly.